This is Pai's stated position as well.
I disagree with you both; I think the two commissions deal with different levels of abstraction and have different regulatory models (prospective licensure vs retrospective enforcement, for example).
However this is a topic on which reasonable people can disagree.
I can see reasonable arguments for supporting regulation under either FCC or FTC. The problem at the moment, as I understand it, is that neither agency has any authority over privacy and security practices of the ISPs.